2003 X, 192 p. 17 illus. Softcover
1-85233-426-6
Special relativity is one of the high points
of the undergraduate
mathematical physics syllabus. Nick Woodhouse
writes for those
approaching the subject with a background
in mathematics: he aims
to build on their familiarity with the foundational
material and
the way of thinking taught in first-year
mathematics courses, but
not to assume an unreasonable degree of prior
knowledge of
traditional areas of physical applied mathematics,
particularly
electromagnetic theory. His book provides
mathematics students
with the tools they need to understand the
physical basis of
special relativity and leaves them with a
confident mathematical
understanding of Minkowski's picture of space-time.
Special
Relativity is loosely based on the tried
and tested course at
Oxford, where extensive tutorials and problem
classes support the
lecture course. This is reflected in the
book in the large number
of examples and exercises, ranging from the
rather simple through
to the more involved and challenging. The
author has included
material on acceleration and tensors, and
has written the book
with an emphasis on space-time diagrams.
Written with the second
year undergraduate in mind, the book will
appeal to those
studying the 'Special Relativity' option
in their Mathematics or
Mathematics and Physics course. However,
a graduate or lecturer
wanting a rapid introduction to special relativity
would benefit
from the concise and precise nature of the
book.
Keywords: Mechanics, Relativity, Special
and General
Contents: Relativity in Classical Mechanics.-
Maxwell's Theory.-
The Propagation of Light.- Einstein's Special
Theory of
Relativity.- Lorentz Transformations in Four
Dimensions.-
Relative Motion.- Relativistic Collisions.-
Relativistic
Electrodynamics.- Tensors and Isometries.-
Notes on Exercises.-
Vector Calculus.- Bibliography.- Index.
Series: Springer Undergraduate Mathematics
Series.
2003 VIII, 429 p. Softcover
3-540-00485-8
The proceedings of the Israeli GAFA seminar
on Geometric Aspect
of Functional Analysis during the years 2001-2002
follow the long
tradition of the previous volumes. They continue
to reflect the
general trends of the Theory. Several papers
deal with the
slicing problem and its relatives. Some deal
with the
concentration phenomenon and related topics.
In many of the
papers there is a deep interplay between
Probability and
Convexity. The volume contains also a profound
study on
approximating convex sets by randomly chosen
polytopes and its
relation to floating bodies, an important
subject in Classical
Convexity Theory. All the papers of this
collection are original
research papers.
Keywords: 46-06, 46B07, 52-06, 60-06, Local
theory of Banach
spaces, Asymptotic geometric Analysis, Convexity
Contents:
Preface.- F. Barthe, M. Csornyei and A. Naor:
A Note on
Simultaneous Polar and Cartesian Decomposition.-
A. Barvinok:
Approximating a Norm by a Polynomial.- S.G.
Bobkov: Concentration
of Distributions of the Weighted Sums with
Bernoullian
Coefficients.- S.G. Bobkov: Spectral Gap
and Concentration for
Some Spherically Symmetric Probability Measures.-
S.G. Bobkov and
A. Koldobsky: On the Central Limit Property
of Convex Bodies.- S.G.
Bobkov and F.L. Nazarov: On Convex Bodies
and Log-Concave
Probability Measures with Unconditional Basis.-
J. Bourgain:
Random Lattice Schrodinger Operators with
Decaying Potential:
Some Higher Dimensional Phenomena.- J. Bourgain:
On Long-Time
Behaviour of Solutions of Linear Schrodinger
Equations with
Smooth Time-Dependent Potential.- J. Bourgain:
On the Isotropy-Constant
Problem for "PSI-2"-Bodies.- E.D.
Gluskin: On the Sum
of Intervals.- E. Gluskin and V. Milman:
Note on the Geometric-Arithmetic
Mean Inequality.- O. Guedon and A. Zvavitch:
Supremum of a
Process in Terms of Trees.- O. Maleva: Point
Preimages under Ball
Non-Collapsing Mappings.- V. Milman and R.
Wagner: Some Remarks
on a Lemma of Ran Raz.- F. Nazarov: On the
Maximal Perimeter of a
Convex Set in R^n with Respect to a Gaussian
Measure.- K.
Oleszkiewicz: On p-Pseudostable Random Variables,
Rosenthal
Spaces and l_p^n Ball Slicing.- G. Paouris:
Psi_2-Estimates for
Linear Functionals on Zonoids.- G. Schechtman,
N. Tomczak-Jaegermann
and R. Vershynin: Maximal l_p^n-Structures
in Spaces with
Extremal Parameters.- C. Schutt and E. Werner:
Polytopes with
Vertices Chosen Randomly from the Boundary
of a Convex Body.-
Seminar Talks (with Related Workshop and
Conference Talks).
Series: Lecture Notes in Mathematics. Volume.
1807
2003 VII, 157 p. Softcover
3-540-00560-9
These notes deal with deformation theory
of complex analytic
singularities and related objects.
The first part treats general theory. The
central notion is that
of versal deformation
in several variants. The theory is developed
both in an abstract
way and in a concrete way suitable for computations.
The second part deals with more specific
problems, specially on
curves and surfaces. Smoothings of singularities
are the main
concern.
Examples are spread throughout the text.
Keywords: Singularity, deformation, versality,
smoothing, quasi-cone
Contents:
Introduction.- Deformations of singularities.-
Standard bases.-
Infinitesimal deformations.- Example: the
fat point of
multiplicity four.- Deformations of algebras.-
Formal deformation
theory.- Deformations of compact manifolds.-
How to solve the
deformation equation.- Convergence for isolated
singularities.-
Quotient singularities.- The projection method.-
Formats.-
Smoothing components of curves.- Kollar's
conjectures.- Cones
over curves.- The versal deformation of hyperelliptic
cones.-
References.- Index.
Series: Lecture Notes in Mathematics. Volume.
1811
2003 XIV, 443 p. Hardcover
0-387-00312-6
This volume is a collection of fourteen papers,
written by well-known
authors, on aspects of applied mathematics,
fluid dynamics,
combustion, kinetic theory, condensed matter
physics,
computational neuroscience, biophysics and
closely related areas.
There are two uniting themes. First, the
papers celebrate the
long and durable contributions of Professor
Lawrence Sirovich on
the occasion of his turning seventy. Second,
the threads of
nonlinearity weave through all the problems
discussed. The papers
combine original research with expository
style and make a
fascinating reading for a diverse readership
in applied
mathematics and science.
Contents: Reading Neural Encodings Using
Phase Space Methods.-
Boolean Dynamics with Random Couplings.-
Oscillatory Binary Fluid
Convection in Finite Containers.- "Solid
Flame" Waves.-
Globally Coupled Oscillator Networks.- Recent
Results in the
Kinetic Theory of Granular Materials.- Variational
Multisymplectic Formulations of Nonsmooth
Continuum Mechanics.-
Geometric Analysis for the Characterization
of Nonstationary Time
Series.- High Conductance Dynamics of the
Primary Visual Cortex.-
Power Law Asymptotics for Nonlinear Eigenvalue
Problems.- A KdV
Model for Multi-Modal Internal Wave Propagation
in Confined
Basins.- A Memory Model for Seasonal Variations
of Temperature in
Mid-Latitudes.- Simultaneously Band and Space
Limited Functions
in Two Dimensions and Receptive Fields of
Visual Neurons.-
Pseudochaos.
2nd ed. 2003 Approx. 630 p. 75 illus. Hardcover
0-387-95576-3
This text builds a solid introduction to
the concepts and
techniques of quantum mechanics in settings
where the phenomena
treated are sufficiently simple that the
student does not face
two fundamental difficulties simultaneously:
viz, that of
learning quantum mechanics and that of learning
how to assess the
validity of models or the reliability of
approximations. The
treatment thus confines itself to systems
that can either be
solved exactly or be handled by well-controlled,
plausible
approximations. With few exceptions, this
means systems with a
small number of degrees of freedom. The exceptions
are a first
pass at many-electron atoms, the electromagnetic
field, and the
Dirac equation. (The inclusion of these last
two topics reflects
the now widely held belief that every physicist
should have at
least a nodding acquaintance with these cornerstones
of modern
physics.)
Born in Vienna, Kurt Gottfried emigrated
to Canada in 1939 and
received his Ph.D. in theoretical physics
from MIT in 1955. He is
professor of physics at Cornell University,
and had previously
been at Harvard University, the Massachusetts
Institute of
Technology, and at CERN in Geneva. He is
the co-author of "Concepts
of Particle Physics" (with V.F. Weisskopf),
and of "The
Fallacy of Star Wars and Crisis, Stability,
and Nuclear War".
Gottfried has an active interest in arms
control and human rights
and is a founder and currently the Chair
of the Union of
Concerned Scientists.
Contents: Fundamental Concepts.- The Formal
Framework.- Basic
Tools.- Low Dimensional Systems.- Hydrogenic
Atoms.- Two-Electron
Atoms.- Symmetries.- Elastic Scattering.-
Inelastic Collisions.-
Electrodynamics.- Systems of Identical Particles.-
Interpretation.-
Relativistic Quantum Mechanics.- Index.
Series: Graduate Texts in Contemporary Physics.